To what degree was the German Luftwaffe successful at repelling Allied bombing raids from 1943 - 45?
The German Luftwaffe was seriously depleted by its efforts in the Battle of Britain in 1940-41 as well as during the war against the USSR on the Eastern Front. In addition, the Allies had an inexhaustible supply of resources and bombers with which to attack Germany. From 1943 on, bombing raids were happening both day and night, and in larger concentrations of bombers. The most the Luftwaffe could do in those circumstances was to thin out the number of attackers and hope the losses became steep enough that the attacks would slow or stop. They very rarely broke up an entire raid.
What's more, the technology of Allied warplanes, both bombers and fighters, became more advanced as the war progressed. By late 1944, the P-51 Mustang (best fighter plane of the war) was in Europe in strength, and had even been equipped with "buddy stores" of fuel so that they could escort the bomber force all the way to their targets and back.
The Luftwaffe, therefore, became less and less successful at protecting the Fatherland from bombing raids as the war went on, and through a brutal process of attrition and loss in addition to critical shortages of parts, pilots and fuel, by early 1945 it had ceased to exist as an effective fighting force.
The Germans had to divert many of their 88 mm. guns from the eastern Front to anti-aircraft use. The allied bombing also diverted vital Luftwaffe assets from the Eastern Front to protect the Fatherland. Until the later part of the war, bombers were sent into Germany without fighter support. Casualtues in the western allied bomber commands reached up to 80% in this period and the air arms overall suffered the highest rate of casualties in the military. So the Germans inflicted high casualties among the allied air, but the superiority of numbers and in production meant that in the war of attrition, even though the allies suffered high casualties, they were able to grind down the German defenses and inflict terrible military and civilian casualties on the Axis.